Optimizing Treatment Using TTFields by Changing the Frequency During the Course of Long Term Tumor Treatment

ABSTRACT

Tumors can be treated with an alternating electric field. The size of cells in the tumor is determined prior to the start of treatment by, for example, biopsy or by inverse electric impedance tomography. A treatment frequency is chosen based on the determined cell size. The cell size can be determined during the course of treatment and the treatment frequency is adjusted to reflect changes in the cell size. A suitable apparatus for this purpose includes a device for measuring the tumor impedance, an AC signal generator with a controllable output frequency, a processor for estimating the size of tumor cells and setting the frequency of the AC signal generator based thereon, and at least one pair of electrodes operatively connected to the AC signal generator such that an alternating electric field is applied to the tumor.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.15/493,309, filed Apr. 21, 2017, which is a continuation-in-part of U.S.application Ser. No. 14/269,784, filed May 5, 2014, which claimspriority to and the benefit of U.S. provisional application 61/819,717,filed May 6, 2013. Each of the above-identified applications isincorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates, generally, to systems and methods foroptimizing the frequency of electromagnetic radiation used in the longterm treatment of tumors.

BACKGROUND OF THE INVENTION

Living organisms proliferate by cell division, including tissues, cellcultures, microorganisms (such as bacteria, mycoplasma, yeast, protozoa,and other single-celled organisms), fungi, algae, plant cells, etc. Whenin the process of dividing, cells of organisms can be destroyed, ortheir proliferation controlled, by methods that are based on thesensitivity of the dividing cells of these organisms to certain chemicalor physical agents.

It is well known that tumors, particularly malignant or canceroustumors, grow uncontrollably compared to normal tissue. Such expeditedgrowth enables tumors to occupy an ever-increasing space and to damageor destroy tissues and organs adjacent thereto. Furthermore, certaincancers are characterized by an ability to spread metastases to newlocations where the metastatic cancer cells grow into additional tumors.

The rapid growth of tumors, in general, and malignant tumors inparticular, as described above, is the result of relatively frequentcell division of these cells compared to normal tissue cells. Thedistinguishably frequent cell division of cancer cells is the basis forthe effectiveness of many existing cancer treatments, e.g., irradiationtherapy and the use of various chemo-therapeutic agents. Such treatmentsare based on the fact that cells undergoing division are more sensitiveto radiation and chemo-therapeutic agents than non-dividing cells.Because tumor cells divide much more frequently than normal cells, it ispossible, to a certain extent, to selectively damage or destroy tumorcells by radiation therapy and/or chemotherapy. The actual sensitivityof cells to radiation, therapeutic agents, etc., is also dependent onspecific characteristics of different types of normal or malignantcells. Unfortunately, in many cases the sensitivity of tumor cells tothe applied therapeutic agent is not sufficiently higher than that ofmany types of normal tissues, therefore existing cancer treatmentstypically cause significant damage to normal tissues, thus limiting thetherapeutic effectiveness of such treatments. Also, certain types oftumors are not sensitive at all to existing methods of treatment.

Electric fields and currents have been used for medical purposes formany years. The most common use is the generation of electric currentsin a human or animal body by application of an electric field by meansof a pair of conductive electrodes between which a potential differenceis maintained. These electric currents are used either to exert theirspecific effects, i.e., to stimulate excitable tissue, or to generateheat by flowing in the body since it acts as a resistor. Examples of thefirst type of application include the following: cardiac defibrillators,peripheral nerve and muscle stimulators, brain stimulators, etc.Currents are used for heating, for example, in devices for tumorablation, ablation of malfunctioning cardiac or brain tissue,cauterization, relaxation of muscle rheumatic pain and other pain, etc.

Another use of electric fields for medical purposes involves theutilization of high frequency oscillating fields transmitted from asource that emits an electric wave, such as an RF wave or a microwavesource, which is directed at the part of the body that is of interest(i.e., a target).

Historically, electric fields used in medical applications wereseparated into two types, namely (1) steady fields or fields that changeat relatively slow rates, and alternating fields of low frequencies thatinduce corresponding electric currents in the body or tissues, and (2)high frequency alternating fields (above 1 MHz) applied to the body bymeans of the conducting electrodes or by means of insulated electrodes.

The first type of electric field has been used, for example, tostimulate nerves and muscles, pace the heart, etc. In fact, such fieldsare used in nature to propagate signals in nerve and muscle fibers, thecentral nervous system (CNS), heart, etc. The recording of such naturalfields is the basis for the ECG, EEG, EMG, ERG, etc. The field strengthin a medium having uniform electric properties is simply the voltageapplied to the stimulating/recording electrodes divided by the distancebetween them. The currents thus generated can be calculated by Ohm'slaw. Those currents, however, can have dangerous stimulatory effects onthe heart and CNS and can result in potentially harmful ionconcentration changes. Also, if the currents are strong enough, they cancause excessive heating in the tissues. This heating can be calculatedby the power dissipated in the tissue (the product of the voltage andthe current).

When such electric fields and currents are alternating, theirstimulatory power (e.g., on nerve, muscle, etc.) is an inverse functionof the frequency. At frequencies above 10 kHz, the stimulation power ofthe field approaches zero. This limitation is due to the fact thatexcitation induced by electric stimulation is normally mediated bymembrane potential changes, the rate of which is limited by theresistive and capacitive properties (with time constants on the order of1 ms) of the membrane.

Regardless of the frequency, when such current inducing fields areapplied, they are often associated with harmful side effects caused bycurrents. For example, one negative effect is the change in ionicconcentration in the various “compartments” within the system, and theharmful products of the electrolysis.

Historically, alternating fields of medium frequencies (about 50 kHz-1MHz) were thought not to have any biological effect except due toheating. But more recently, the usefulness of such fields has beenrecognized, particularly when the fields are applied to a conductivemedium, such as a human body, via insulated electrodes. Under suchconditions the electrodes induce capacitive currents in the body. InU.S. Pat. No. 7,016,725, 7,089,054, 7,333,852, 7,805,201, and 8,244,345by Palti (each of which is incorporated herein by reference) and in apublication by Kirson (see Eilon D. Kirson, et al., Disruption of CancerCell Replication by Alternating Electric Fields, Cancer Res. 200464:3288-3295), such fields have been shown to have the capability tospecifically affect cancer cells and serve, among other uses, fortreating cancer. These fields are referred to herein as TTFields.

The above listed references demonstrate that the efficacy of alternatingfields in specifically damaging cancer cells is frequency dependent, andalso demonstrate that the optimal frequency is different for differentcell types. Thus for example the optimal frequency for malignantmelanoma tumor cells is 100 kHz, while that for Glioblastoma multiformeis 200 kHz. It was further demonstrated that these differences resultfrom the differences in cell size as shown in another publication byKirson (see Kirson E D, Dbaly V, Tovarys F, et al. Alternating electricfields arrest cell proliferation in animal tumor models and human braintumors. Proc Natl Acad Sci U.S.A. 2007; 104:10152-10157). Thus for eachtype of cancer, treatment is preferably given at a particular optimalfrequency.

The frequency used for the treatment is based on the inverserelationship between the cell size and the optimal treatment frequencyas calculated by Kirson (see Kirson E D, Dbaly V, Tovarys F, et al.Alternating electric fields arrest cell proliferation in animal tumormodels and human brain tumors. Proc Natl Acad Sci U S A.2007;104:10152-10157) on the basis of the maximal electric force exertedon the polar particles in the dividing tumor cell (during cytokinesis)is depicted in FIG. 1. Note that the experimentally determined optimaltreatment frequency and histological measurements of cell size inmelanoma and glioma fall reasonably well on the calculated curve.

One shortcoming of previous approaches as described above, is the use ofa single fixed frequency throughout the treatment of a tumor. While thefrequency may be optimal at the start of the treatment, previousapproaches did not take into account the possibility that the cells inthe tumor may change size as the treatment progresses. Thus, previousapproaches failed to optimize the frequency of radiation directed at thetumor throughout the treatment process.

SUMMARY OF THE INVENTION

The embodiments described herein provide a second-order improvement tothe Palti and Kirson advances, based on the inventor's recognition thatduring the course of treatment for a particular type of cancer, theaverage cell size may not remain constant. As a result, the efficacy ofthe treatment may be improved by optimizing the frequency over timeduring the treatment to match expected changes in the cell size thatoccur over time.

An apparatus and related method for optimizing cancer treatment withTTFields are provided. Optimization is achieved by adjusting thefrequency of the alternating electric field to the value that isclinically optimal for the specific tumor in the individual patient atdifferent times during the course of treatment. The basis of the methodis the fact that the maximal exerted force on cell components byelectric field forces including dielectrophoresis forces is both cellsize and frequency dependent. As a result there is an optimal treatmentfrequency that is dependent on the specific tumor cell size at any givenmoment in time. Moreover, since the cell size changes over time, thefrequency should be changed to compensate for the changes in the cellsize to maintain the most effective treatment.

In one aspect, the invention features a method for adaptively treating atumor with an alternating electric field. The method involves applyingan alternating electric field having a first frequency to the tumor. Themethod further involves determining an impedance of the tumor based on ameasured current while the alternating electric field having the firstfrequency is applied. Additionally, the method involves estimating asize of cells in the tumor based on the determined impedance. The methodalso involves selecting a second frequency based on the estimated sizeof cells. Thus, determination of the impedance leads to selection of thetreatment frequency. Moreover, the method involves applying analternating electric field to the tumor at the second frequency to treatthe tumor.

In some embodiments, the method involves waiting for a period of time.The method further involves applying an alternating electric fieldhaving a third frequency to the tumor. The method further involvesdetermining a second impedance of the tumor based on a measured currentwhile the alternating electric field having the third frequency isapplied. The method further involves estimating a second size of cellsin the tumor based on the determined second impedance. The methodfurther involves selecting a fourth frequency based on the estimatedsecond size of cells. The method further involves applying analternating electric field to the tumor at the fourth frequency to treatthe tumor.

In some embodiments, the method further involves waiting for a period ofat least one week. In some embodiments, the method further involvesdetermining a size, shape, type, or location of the tumor. In someembodiments, the method further involves estimation of the size of cellsbased on a Cole-Cole plot. In some embodiments, the method furtherinvolves imaging the tumor with CT, MM, or PET to locate portions of thetumor not having excess blood or cyst fluid and estimating the size ofcells based on a measured impedance of the located portions.

In another aspect, the invention relates to an apparatus for adaptivelytreating a tumor with electromagnetic radiation. The apparatus includesan electrical impedance tomography device for measuring the impedance ofthe tumor, the electrical impedance tomography device using a frequencysuch that a size of cells in the tumor can be determined from themeasured impedance of the tumor. The apparatus also includes an ACsignal generator having a controllable output frequency. The apparatusalso includes a processor for estimating the size of cells in the tumorbased on the measured impedance of the tumor and setting the frequencyof the AC signal generator based on the estimated size of cells in thetumor. The apparatus also at least one pair of electrodes operativelyconnected to the AC signal generator such that an alternating electricfield is applied to the tumor to selectively destroy cells in the tumor.

In some embodiments, the size of cells in the tumor is determined basedon a Cole-Cole plot. In some embodiments, the apparatus further includesa CT, MRI, or PET imaging device configured to locate portions of thetumor not having excess blood or cyst fluid; and wherein the electricalimpedance tomography device only measures the impedance of the locatedportions. In some embodiments, the electrical impedance tomographydevice is configured to make periodic impedance measurements. In someembodiments, the periodicity of the impedance measurements is at leastone week. In some embodiments, the periodicity of the impedancemeasurements is at least one month. In some embodiments, the periodicityof the impedance measurements is based on a history of the tumor. Insome embodiments, the periodicity of the impedance measurements is basedon the type of tumor. In some embodiments, the frequency of the ACsignal generator is set based on a spectrum of cell sizes. In someembodiments, the frequency of the AC signal generator is set based on anaverage cell size. In some embodiments, the processor computes a size ofcells in the tumor based on a database look-up table.

In yet another aspect, the invention relates to a method for adaptivelytreating a tumor with an alternating electric field. The method involvesdetermining a first size of cells in the tumor. The method also involvesselecting a first frequency based on the determined first size. Themethod also involves applying an alternating electric field to the tumorat the first frequency to treat the tumor. The method also involveswaiting a period of time and subsequently determining a second size ofcells in the tumor. The method also involves selecting a secondfrequency based on the determined second size. The method also involvesapplying an alternating electric field to the tumor at the secondfrequency to treat the tumor.

In some embodiments, the method further involves the first size and thesecond size being determined based on a tumor biopsy. In someembodiments, the method further involves the first size and the secondsize being determined based on a measured impedance of the tumor. Insome embodiments, the method further involves the determinations of thefirst size and the second size being made based on a Cole-Cole plot. Insome embodiments, the method further involves imaging the tumor with CT,MRI, or PET to locate portions of the tumor not having excess blood orcyst fluid and determining the first size and the second size based on ameasure impedance of the located portions. In some embodiments, themethod further involves wherein the tumor is a glioma tumor or amelanoma tumor. In some embodiments, the method further involves whereinthe period of time is at least one week. In some embodiments, the methodfurther involves wherein the period of time is at least one month. Insome embodiments, the method further involves wherein the firstfrequency and the second frequency are selected based on an average cellsize. In some embodiments, the method further involves wherein the firstfrequency and the second frequency are selected based on a spectrum ofcell sizes. In some embodiments, the method further involves wherein theperiod of time is chosen based on the type of tumor. In someembodiments, the method further involves wherein the period of time ischosen based on the history of the tumor. In some embodiments, themethod further involves wherein the first size and the second size aredetermined based on a database look-up table.

In yet another aspect, the invention relates to a method for adaptivelyproviding a medical treatment to a patient. The method involves applyingan alternating electric field to a group of patient cells. The methodalso involves determining an impedance of the group of patient cellsbased on a measured current while the alternating electric field isapplied. The method also involves selecting a treatment parameter basedon the determined impedance. The method also involves applying atreatment to the patient in accordance with the selected treatmentparameter.

In some embodiments, the method further involves waiting for a period oftime. The method further involves applying an alternating electric fieldto a group of patient cells. The method further involves determining asecond impedance of the group of patient cells based on a measuredcurrent while the alternating electric field is applied. The methodfurther involves selecting a second treatment parameter based on thedetermined second impedance. The method further involves applying atreatment to the patient in accordance with the selected secondtreatment parameter.

In some embodiments, the method further involves estimating a size ofcells in the group of patient cells based on the determined impedance orthe determined second impedance. The method further involves selecting atreatment parameter based on the estimated size of cells. In someembodiments, the medical treatment is chemotherapy. In some embodiments,the medical treatment is a surgery or therapy. In some embodiments, thetherapy is acoustic therapy, pharmacotherapy, radiation therapy, ornutritional therapy.

Yet another aspect of the invention is directed to a first apparatus foradaptively treating a tumor with an alternating electric field. Thefirst apparatus comprises an AC signal generator, at least one pair ofelectrodes, an electrical impedance tomography device, and a processor.The AC signal generator has an output. The at least one pair ofelectrodes is operatively connected to the output of the AC signalgenerator such that an alternating electric field is applied to thetumor to selectively destroy cells in the tumor, and the AC signalgenerator is configured to apply a first alternating electrical signalto the output for a first period of time. The electrical impedancetomography device measures an impedance of the tumor to account forexpected changes that occur as a result of treating the tumor for thefirst period of time. The processor is configured to adjust a parameterof treatment based on the measured impedance of the tumor after thefirst period of time, and further configured to account for changes inthe tumor that have occurred during the first period of time bycontrolling the AC signal generator so that the AC signal generatorapplies a second alternating electrical signal to the output for asecond period of time using the adjusted parameter of treatment. Thesecond period of time is subsequent to the first period of time.

In some embodiments of the first apparatus, the parameter of treatmentis an operating frequency of the AC signal generator. In someembodiments of the first apparatus, the first alternating electricalsignal has a first frequency, and wherein the second alternatingelectric signal has a second frequency that is different from the firstfrequency. In some embodiments of the first apparatus, the AC signalgenerator and the electrical impedance tomography device are separatedevices.

Another aspect of the invention is directed to a first method foradaptively treating a tumor with an alternating electric field. Thefirst method comprises applying a first alternating electric field tothe tumor for a first period of time to selectively destroy cells in thetumor; and measuring an impedance of the tumor to account for expectedchanges that occur as a result of treating the tumor for the firstperiod of time. The first method also comprises adjusting a parameter oftreatment based on the measured impedance of the tumor after the firstperiod of time to account for changes in the tumor that have occurredduring the first period of time; and applying a second alternatingelectric field to the tumor for a second period of time to selectivelydestroy cells in the tumor, wherein the second alternating electricfield uses the adjusted parameter of treatment. The second period oftime is subsequent to the first period of time.

In some instances of the first method, the parameter of treatment is anoperating frequency. In some instances of the first method, the firstalternating electrical field has a first frequency, and the secondalternating electric field has a second frequency that is different fromthe first frequency.

BRIEF DESCRIPTION OF THE DRAWINGS

The advantages of the invention described above, together with furtheradvantages, may be better understood by referring to the followingdescription taken in conjunction with the accompanying drawings. Thedrawings are not necessarily to scale, emphasis instead generally beingplaced upon illustrating the principles of the invention.

FIG. 1 is a graph of a calculated relationship between the cell radiusand the optimal treatment frequency according to an illustrativeembodiment of the invention.

FIG. 2 is a graph showing cell volume in picoliters (pL) plotted againsttime in hours (h) according to an illustrative embodiment of theinvention.

FIG. 3 is an image showing a normal breast and a breast with a tumoraccording to an illustrative embodiment of the invention.

FIG. 4 is an image of a tumor and surrounding tissue according to anillustrative embodiment of the invention.

FIG. 5 is an image showing a geometrical model representation for cellsin a tissue according to an illustrative embodiment of the invention.

FIG. 6 is a diagram showing an RC circuit equivalent of a PCIC modelaccording to an illustrative embodiment of the invention.

FIG. 7 is a graph showing the real part of the impedance plotted againstcell diameter for a variety of different frequencies according to anillustrative embodiment of the invention.

FIG. 8 is a graph showing the real part of the impedance plotted againstcell diameter for a variety of different frequencies according to anillustrative embodiment of the invention.

FIG. 9 is a graph showing the real and imaginary parts of the impedanceplotted against frequency for a variety of different cell diametersaccording to an illustrative embodiment of the invention.

FIG. 10 is a graph showing a Cole-Cole plot according to an illustrativeembodiment of the invention.

FIG. 11 is a flow chart illustrating a method in accordance with oneembodiment for adjustment the treatment frequency during the course oftumor treatment in accordance with an illustrative embodiment of theinvention.

FIG. 12 is a diagram of an apparatus for adjusting the treatmentfrequency of a tumor during the course of treatment according to anillustrative embodiment of the invention.

FIG. 13 is a table of parameters used in the calculations shown in FIGS.7-9.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

In preferred embodiments of the invention, the size of cells in a tumoris determined throughout a treatment process utilizing TTFields. Thefrequency of the TTFields is then optimized based on the determined cellsize. One way to determine the cell size (step 1120 in FIG. 11) is tofirst take impedance measurements, and then use those impedancemeasurements to compute the cell size. The tumor impedance can bedetermined, for example, by in-vivo MRI electrical impedance tomography(MREIT), or by following a new tumor impedance estimation method whichmay be termed “Inverse Electric Impedance Tomography” that is carriedout as follows:

At the initial stage of the impedance estimation a CT, MRI, PET, orequivalent body/tissue imaging is made of the patient's tumor within itsnatural surrounding area. This image serves to determine the tumorlocation, size, shape, etc. relative to specific body markers.

Next, electrical impedance tomography (EIT) of the tumor together withthe surrounding area is carried out by conventional means. As is wellknown, Standard EIT is carried out by applying an alternating electricfield of selected frequencies to the body in the relevant area byappropriate electrodes while measuring the surface potentialdistribution by means of additional electrodes. On the basis of thisinformation a 3D image of the impedance of the selected area isconstructed, as illustrated in FIG. 3. This type of procedure isnormally done in order to determine whether there is a tumor(characterized by an area with impedance that is different from thenormal surroundings) in the scanned area. When this measurement iscarried out within the framework of the “Inverse Electric ImpedanceTomography” the standard alternating field/current frequency is replacedby one that is best suited for cell size determination.

It is important to note that EIS/EIT produces an impedance map of anobject based upon the spatial electrical characteristics throughout thevolume of the object. When a current is injected into an object, byOhm's law the voltage drop will be proportional to the impedance of theobject as long as the object has passive electrical characteristics. InEIS, a known current is injected into the surface and the voltage ismeasured at a number of points (electrodes) on the surface of theobject. The resolution of the resultant image is dependent on the numberof electrodes. Areas of low impedance typically appear on an EIS map asareas that have greater intensity (whiter). A measure of the electricalproperties of the volume within the surface is obtained from these maps.An example of a device designed to detect tumors by EIT is the SiemensTS2000.

In this embodiment, an “inverse process” is being carried out asfollows: In stage one above the existence and location of the tumor havebeen established using CT, MRI, PET, etc. The tumor coordinates thusobtained are provided to the processor that constructs the EIT image sothat it will provide the calculated the average impedance values atselected tumor area as depicted in FIG. 4.

The impedance values of the specific tumor areas are registered forcomparison with subsequent values obtained at later times. Note that theimpedance is a function of the alternating field frequency used in theEIT. The impedance of the selected tumor area is now converted toaverage cell size or a spectrum of cell sizes on the basis of theelectric impedance vs. cell size curves or tables of the relevant tumor,if available, or otherwise, on the calculations based on a geometric orPrismatic Cell in a Cube (PCIC) model.

FIG. 1 shows a graph 100 that includes a calculated relationship 104between the cell radius (μm) and the optimal treatment frequency (kHz)as calculated on the basis of the maximal electric force exerted on thepolar particles in the dividing tumor cell (during cytokinesis). FIG. 1also shows experimentally determined treatment frequencies for glioma108 and melanoma 112. Note that the experimentally determined optimaltreatment frequencies and histological measurements of cell size inmelanoma and glioma fall reasonably well on the calculated curve.

FIG. 2 shows a graph 200 of cell volume in picoliters (pL) plottedagainst time in hours (h). FIG. 2 illustrates how the cell size canchange over time in a cell culture of A2780 human ovarian cancer cellline exposed to TTFields. It can be seen that in this case during thefirst 72 hours of treatment the cell volume increases. For example, FIG.2 shows that for cells not exposed to TTFields (curve 204), the cellvolume remains approximately constant, having a value of about 2 pL.Additionally, FIG. 2 shows that for cells exposed to TTFields (curves201-203), the cell volume increase from a value of about 2 pL to a valueof about 3 pL over the course of about 72 hours. Similarly, during longduration treatment in vivo, the cell volume changes may also differ. Forexample, in one patient who had three GBM biopsies over a period of twoyears of treatment with TTFields, histological sections indicated a 30%decrease in cell volume. In view of these volume changes with time, afrequency adjustment procedure is preferably repeated during the courseof treatment (e.g., every few weeks or months), preferably depending onthe type of tumor and the history of the tumor in the specific patient.

FIG. 3 shows an image 300 of a normal breast 304 and an image of abreast with a tumor 308. The images 304 and 308 can be acquired byx-ray, computed tomography (CT), magnetic resonance imaging (MM),positron emission tomography (PET), or equivalent. The breast tumor 312appears as a white patch within image 308. The image 308 shows theshape, size, type, and location of the tumor 312.

FIG. 4 is a graph 400 of an electric impedance tomography (EIT) image ofa tumor together with the surrounding areas, showing the electricalconductivity (S/m) of the imaged region plotted against position (m).The tumor is located in the rectangular region 404 of the graph.

FIG. 5 shows a geometrical model representation 500 for cells in atissue. Following Gimsa (A unified resistor-capacitor model forimpedance, dielectrophoresis, electrorotation, and induced transmembranepotential. Gimsa J, Wachner D. Biophys J. 1998 August; 75(2): 1107-16.),the tissue can be modeled as elementary cubes 504, in which eachelementary cube 504 is embedded with an elementary cell of prismaticgeometry 508. The model representation 500 can be referred to as aprismatic cell in a cube model (PCIC). The geometrical model 500 can bemirror symmetric on the mid-plane of the cube.

FIG. 6 shows an RC circuit 600 (i.e. a circuit containing resistors andcapacitors) equivalent of a PCIC model, corresponding to one half of theprismatic cell in a cube. For a homogeneous medium, i, which containsthe following tissue/cell elements: intracellular medium, extracellularmedium and outer cell membrane, the impedance is modeled as a parallelRC circuit with a corresponding impedance (FIG. 6):

$Z_{i} = \frac{L_{i}}{\sigma_{i}^{*}A_{i}}$

where, L_(i), A₁, and σ_(i)* are the length in parallel to the current,the area perpendicular to the current and the complex conductivity ofmedium i, respectively.

The complex conductivity can be modeled as:

σ_(i)*=σ_(i) +jωε _(i)ε_(o)

The equivalent RC circuit can be used to model a homogeneous medium thatcontains an intracellular medium 603, extracellular medium 601, andouter cell membrane 602. In cases where the geometrical model is mirrorsymmetric on the mid-plane of the cube, such as is shown in FIG. 5, theimpedance of only one half of the equivalent circuit needs to be solvedand the total impedance is just twice the calculated one.

FIGS. 7-9 show graphs of the real and imaginary parts of the impedanceas a function of cell diameter of the constituent cells for a range ofelectromagnetic frequencies between 1 kHz and 1 MHz used during theimpedance measurement. FIG. 7 shows a graph 700 of the real component ofimpedance plotted against cell diameter for a variety of electromagneticfrequencies. For example, curves 701, 702, 703, 704, 705, 706, 707, 708,709, 710, 711, 712, 713, 714, 715, 716, 717, 718, and 719 correspond toelectromagnetic frequencies of 1 kHz, 2 kHz, 3 kHz, 4 kHz, 6 kHz, 9 kHz,13 kHz, 18 kHz, 26 kHz, 38 kHz, 55 kHz, 78 kHz, 113 kHz, 162 kHz, 234kHz, 336 kHz, 483 kHz, 695 kHz, and 1000 kHz, respectively. FIG. 8 showsa graph 800 of the imaginary component of impedance plotted against celldiameter for a variety of electromagnetic frequencies. For example,curves 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813,814, 815, 816, 817, 818, and 819 correspond to electromagneticfrequencies of 1 kHz, 2 kHz, 3 kHz, 4 kHz, 6 kHz, 9 kHz, 13 kHz, 18 kHz,26 kHz, 38 kHz, 55 kHz, 78 kHz, 113 kHz, 162 kHz, 234 kHz, 336 kHz, 483kHz, 695 kHz, and 1000 kHz, respectively. FIG. 9 shows a graph 900 ofboth the real and imaginary parts of the impedance plotted againstfrequency different cell diameters of constituent cells. For example,curves 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, and 911correspond to the real part of the impedance for cell diameters of 5 μm,6 μm, 7 μm, 8 μm, 9 μm, 10 μm, 13 μm, 16 μm, 19 μm, 22 μm, and 25 μm,respectively. Additionally, curves 912, 913, 914, 915, 916, 917, 918,919, 920, 921, and 922 correspond to the imaginary part of the impedancefor cell diameters of 5 μm, 6 μm, 7 μm, 8 μm, 9 μm, 10 μm, 13 μm, 16 μm,19 μm, 22 μm, and 25 μm, respectively. FIG. 10 shows a graph 1000 of thereal part of the impedance plotted against the imaginary part of theimpedance for a variety of different cell diameters of constituentcells. For example, curves 1001, 1002, 1003, 1004, 1005, 1006, 1007,1008, 1009, 1010, and 1011 correspond to cell diameters of 5 μm, 6 μm, 7μm, 8 μm, 9 μm, 10 μm, 13 μm, 16 μm, 19 μm, 22 μm, and 25 μmrespectively. The curves 1001-1011 further contain information about theelectromagnetic frequency applied to the constituent cells. From rightto left, the frequency increases along the clockwise direction of thecurve from about 100 Hz on the far right, to about 1 MHz on the farleft. A Cole-Cole plot as shown in FIG. 10 can be constructed based onthe data shown in FIGS. 7-9.

Once the impedance of the tumor is known, FIGS. 7-9 can be used to inferthe cell size. The impedance of an array of PCIC blocks, i.e. the IMP,can be easily deduced from the impedance of one PCIC block, the imp,through:

${IMP} = {{\frac{\left( \frac{D}{a} \right)}{\left( \frac{D}{a} \right)^{2}}{imp}} = {\frac{a}{D}{imp}}}$

where D is the side length of a cube of the tissue (or tumor) and a isthe side length of the PCIC block. It is important to note that FIGS.7-9 indicate that there are preferable frequencies that should be usedin the impedance tomography. As seen, for example, in FIG. 7 up tofrequencies of about 30 kHz the impedance (real component) vs. cell sizecurves have a peak, i.e. there are cell sizes with the same impedance(two relevant solutions to the equations) leaving an ambiguity as to theactual size. However, for higher frequencies the curves are monotonousand there is a unique solution/size corresponding to each impedancevalue. Thus the impedance tomography should preferably be performed atfrequencies that provide unique cell sizes. Once the cell size isdetermined, the optimal treatment frequency can be determined on thebasis of curves such as those depicted in FIG. 1. Note that for thecalculations presented in FIGS. 7-9, the elementary cube of tissue (ortumor) is chosen to have a size of 1 mm. Other parameters used in thecalculations shown in FIG. 7-9 can be found in Table 1 as shown in FIG.13. In alternative embodiments, the data from FIG. 10 can be used toinfer the cell size once the impedance has been determined.

Note that viewing the data from FIG. 10 and FIG. 1 together leads to theconclusion that a direct relationship exists between measured impedanceand the desirable treatment frequency, such that the treatment frequencycan be determined directly from the measured impedance.

FIG. 10 shows a Cole-Cole plot that can be used to determine the size ofa cell based on an impedance measurement. The Cole-Cole plot shows theimpedance spectrum of the constituent cells as a function of the celldiameter. Note that in cases where both the tumor cell size, area ofnecrosis, cyst or level of vascularization change with time a potentialerror may be introduced by the impedance changes resulting from thechanges in fluid or blood volume within the tumor. This can be correctedfor along two pathways. When the fluid (blood, cyst fluid) volume islarge enough, it can be detected by the CT and the impedance tomographyimages and thus non affected areas can be selected for the computation.Alternatively corrections can be made on the basis of the fact that thecell membranes of the cell mass have both capacitive and resistive i.e.real & imaginary components while the fluids and blood are, to a goodapproximation, primarily resistive elements. Here the correction isbased on the construction of a Cole-Cole plot (see the example given inFIG. 10) from the tumor impedance values as determined by impedancetomography. In our case, these measurements are carried out atfrequencies in the range dictated by the requirements of the Cole-Coleplot for tissue rather than by the optimal frequency requirements ofimpedance tomography. Note that the changes in the blood content of thetumor will be reflected mainly in the resistive aspect of the Cole-Coleplot. Utilizing the ratio between the impedance of the tumor and thetissue surrounding the tumor may add to the accuracy.

FIG. 11 shows a method for adaptively treating a tumor withelectromagnetic radiation. The method includes determining a cell size(step 1110). The cell size can be determined by first locating the tumorby a conventional imaging method, such as CT, Mill, or PET. The cellsize can also be determined from histological sections made of samplesobtained by biopsies of the tumor taken from the specific patient. Thecell size can also be predicted based on the type of cancer involved.After locating the tumor, inverse electrical impedance tomography (IEIT)of the tumor together with the surrounding area can be performed. As iswell known, Standard EIT is carried out by applying an alternatingelectric field of selected frequencies to the body in the relevant areaby appropriate electrodes while measuring the surface potentialdistribution by means of additional electrodes.

On the basis of this information a 3D image of the impedance of theselected area is constructed, as illustrated in FIG. 4. This type ofprocedure is normally done in order to determine whether there is atumor (characterized by an area with impedance that is different fromthe normal surroundings) in the scanned area. When this measurement iscarried out within the framework of the IEIT, the standard alternatingfield/current frequency is replaced by one that is best suited for cellsize determination. FIGS. 7-10 show exemplary frequencies suitable forcarrying out IEIT.

For example, referring to FIG. 7, a frequency of 38 kHz (correspondingto curve 711) may be preferable when determining cell size via IEIT. Themethod also includes setting a frequency based on the determined cellsize (step 1120). The frequency can be selected on the basis of curvessuch as those depicted in FIG. 1. The treatment frequency adjustmentpreferably occurs before the initialization of treatment and accordingto this embodiment readjustment continues during the treatment, theduration of which may be months and even years. The method also includestreating the tumor for an interval of time (step 1130), using the newtreatment frequency. In some embodiments, the treatment frequency caninclude two or more frequencies that can be applied to the tumor eithersequentially or simultaneously. The initial setting of the frequency ispreferably selected by first determining or estimating the average sizeof the tumor cell and spectrum of cell sizes in step 1110.

In a particular embodiment, three frequencies are provided in aninterleaved fashion, such that first frequency F1 is applied for aperiod of time, then second frequency F2 is applied for a period oftime, and then third frequency F3 is applied for a period of time. Thenthe cycle repeats, starting again with F1. The duration of each timeperiod can be different for each frequency, but in an embodiment thetime periods are the same. This treatment allows simultaneous treatmentof different types of tumors, or treating a tumor with different cellsizes.

The initial size is preferably determined from histological sectionsmade of samples obtained by biopsies of the tumor taken from thespecific patient. But it can also be set using a prediction that isbased on the type of cancer or using the impedance approach described inrelation to FIGS. 7-9. After a suitable interval of time has elapsed(e.g., a few weeks or months), a decision to continue treatment is made(step 1140). If the treatment is to be continued, processing returns tostep 1110, where the next cell size determination is made. Otherwise,the treatment adjustment ends. The tumor cell size is preferablyevaluated periodically, e.g., every 1-3 months, preferably using one ormore of the following three approaches: (1) tumor biopsies, (2) thenovel algorithms described herein that relate the cell size to thepatient's tumor impedance as determined by special procedures, or (3) adata base look-up table. If the cell size has changed, the treatingfield frequency is adjusted accordingly in step 1120. The new treatmentfrequency is then used in step 1130.

FIG. 12 is a block diagram of a system that can apply TTFields with thedifferent frequencies to the patient. The core of the system is an ACsignal generator 1200 whose output is hooked up to at least one pair ofelectrodes E1. Preferably, at least one additional pair of electrodes E2is also hooked up to additional outputs of the signal generator. Thesignals are preferably applied to the different pairs of electrodessequentially in order to switch the direction of the electric field, asdescribed in U.S. Pat. No. 7,805,201.

The AC signal generator 1200 has a control that changes the frequency ofthe signals that are generated. In some embodiments, this control can beas simple as a knob that is built in to the signal generator. But morepreferably, the AC signal generator 1200 is designed to respond to asignal that arrives on a control input, and the frequency control 1202sends a suitable signal (e.g., an analog or digital signal) to thecontrol input of the AC signal generator 1200 to command the signalgenerator to generate an output at the desired frequency. The frequencycontrol 1202 can send a frequency to the AC signal generator 1200 basedon a measured or estimated cell diameter. The cell diameter can bedetermined by a histological measurement or by IEIT.

Once the cell diameter is determined, an optimal treatment frequency canbe determined. The frequency control 1202 can then send a control signalto the AC signal generator 1200 to set the frequency of the AC signalgenerator to the optimal treatment frequency. A processor can be coupledto the frequency control 1202 to automate the process of selecting anoptimal treatment frequency based on a measured or estimated celldiameter. The processor can receive information about the measured orestimated cell size and then determine an optimal treatment frequencybased on the received information. After determining an optimaltreatment frequency, the processor can send a control signal to thefrequency control 1202 that causes the frequency control 1202 to send asignal the AC signal generator 1200 that causes the AC signal generatorto output the optimal treatment frequency.

While the embodiments described thus far have been focused on adaptivelytreating a tumor with TTFields, the invention has broader implications.In various embodiments, IEIT could be used to measure the impedance of agroup of patient cells. The determined impedance of the group of patientcells could then be used to adjust a parameter of the treatment. Thetreatment could be a surgery or a therapy such as chemotherapy,radiation therapy, pharmacotherapy, or nutritional therapy. In someembodiments, the determined impedance of the patient cells can be usedto estimate the size of cells in the group of patient cells. A parameterof the treatment could then be adjusted based on the estimated cellsize.

The terminology used herein is for the purpose of describing particularembodiments and is not intended to be limiting of the inventiveconcepts. It will be understood that, although the terms first, second,third etc. are used herein to describe various elements, components,regions, layers and/or sections, these elements, components, regions,layers and/or sections should not be limited by these terms. These termsare only used to distinguish one element, component, region, layer orsection from another element, component, region, layer or section. Thus,a first element, component, region, layer or section discussed belowcould be termed a second element, component, region, layer or sectionwithout departing from the teachings of the present application.

While the present inventive concepts have been particularly shown anddescribed above with reference to exemplary embodiments thereof, it willbe understood by those of ordinary skill in the art, that variouschanges in form and detail can be made without departing from the spiritand scope of the present inventive concepts described and defined by thefollowing claims.

What is claimed is:
 1. An apparatus for adaptively treating a tumor withan alternating electric field, the apparatus comprising: an AC signalgenerator having an output; at least one pair of electrodes operativelyconnected to the output of the AC signal generator such that analternating electric field is applied to the tumor to selectivelydestroy cells in the tumor, wherein the AC signal generator isconfigured to apply a first alternating electrical signal to the outputfor a first period of time; an electrical impedance tomography devicefor measuring an impedance of the tumor to account for expected changesthat occur as a result of treating the tumor for the first period oftime; and a processor configured to adjust a parameter of treatmentbased on the measured impedance of the tumor after the first period oftime, and further configured to account for changes in the tumor thathave occurred during the first period of time by controlling the ACsignal generator so that the AC signal generator applies a secondalternating electrical signal to the output for a second period of timeusing the adjusted parameter of treatment, wherein the second period oftime is subsequent to the first period of time.
 2. The apparatus ofclaim 1, wherein the parameter of treatment is an operating frequency ofthe AC signal generator.
 3. The apparatus of claim 1, wherein the firstalternating electrical signal has a first frequency, and wherein thesecond alternating electric signal has a second frequency that isdifferent from the first frequency.
 4. The apparatus of claim 1, whereinthe AC signal generator and the electrical impedance tomography deviceare separate devices.
 5. A method for adaptively treating a tumor withan alternating electric field, the method comprising: applying a firstalternating electric field to the tumor for a first period of time toselectively destroy cells in the tumor; measuring an impedance of thetumor to account for expected changes that occur as a result of treatingthe tumor for the first period of time; adjusting a parameter oftreatment based on the measured impedance of the tumor after the firstperiod of time to account for changes in the tumor that have occurredduring the first period of time; and applying a second alternatingelectric field to the tumor for a second period of time to selectivelydestroy cells in the tumor, wherein the second alternating electricfield uses the adjusted parameter of treatment, wherein the secondperiod of time is subsequent to the first period of time.
 6. The methodof claim 5, wherein the parameter of treatment is an operatingfrequency.
 7. The method of claim 5, wherein the first alternatingelectrical field has a first frequency, and wherein the secondalternating electric field has a second frequency that is different fromthe first frequency.